On manifest SU(4)-invariant superstring action in AdS(5) x S-5

We discuss manifestly SL(2, C) x SU(4) and kappa -invariant superstring act ion in an AHS(5) x S-5 background within the framework of the Green-Schwarz formulation. The action is formulated in terms of 16 Poincare fermionic co ordinates which through AdS/CFT correspondence should represent N = 4 SYM s uperspace and 16 superconformal fermionic coordinates. The action is also m anifestly invariant with respect to the usual N = 4 Poincare superalgebra t ransformations. kappa -symmetry gauge fixing and the derivation of lightcon e gauge action are simplified.